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Grafika_2024/dependencies/glm/gtc/matrix_transform.inl

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/// @ref gtc_matrix_transform
/// @file glm/gtc/matrix_transform.inl
#include "../geometric.hpp"
#include "../trigonometric.hpp"
#include "../matrix.hpp"
namespace glm
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> translate(tmat4x4<T, P> const & m, tvec3<T, P> const & v)
{
tmat4x4<T, P> Result(m);
Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate(tmat4x4<T, P> const & m, T angle, tvec3<T, P> const & v)
{
T const a = angle;
T const c = cos(a);
T const s = sin(a);
tvec3<T, P> axis(normalize(v));
tvec3<T, P> temp((T(1) - c) * axis);
tmat4x4<T, P> Rotate(uninitialize);
Rotate[0][0] = c + temp[0] * axis[0];
Rotate[0][1] = temp[0] * axis[1] + s * axis[2];
Rotate[0][2] = temp[0] * axis[2] - s * axis[1];
Rotate[1][0] = temp[1] * axis[0] - s * axis[2];
Rotate[1][1] = c + temp[1] * axis[1];
Rotate[1][2] = temp[1] * axis[2] + s * axis[0];
Rotate[2][0] = temp[2] * axis[0] + s * axis[1];
Rotate[2][1] = temp[2] * axis[1] - s * axis[0];
Rotate[2][2] = c + temp[2] * axis[2];
tmat4x4<T, P> Result(uninitialize);
Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2];
Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2];
Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2];
Result[3] = m[3];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate_slow(tmat4x4<T, P> const & m, T angle, tvec3<T, P> const & v)
{
T const a = angle;
T const c = cos(a);
T const s = sin(a);
tmat4x4<T, P> Result;
tvec3<T, P> axis = normalize(v);
Result[0][0] = c + (static_cast<T>(1) - c) * axis.x * axis.x;
Result[0][1] = (static_cast<T>(1) - c) * axis.x * axis.y + s * axis.z;
Result[0][2] = (static_cast<T>(1) - c) * axis.x * axis.z - s * axis.y;
Result[0][3] = static_cast<T>(0);
Result[1][0] = (static_cast<T>(1) - c) * axis.y * axis.x - s * axis.z;
Result[1][1] = c + (static_cast<T>(1) - c) * axis.y * axis.y;
Result[1][2] = (static_cast<T>(1) - c) * axis.y * axis.z + s * axis.x;
Result[1][3] = static_cast<T>(0);
Result[2][0] = (static_cast<T>(1) - c) * axis.z * axis.x + s * axis.y;
Result[2][1] = (static_cast<T>(1) - c) * axis.z * axis.y - s * axis.x;
Result[2][2] = c + (static_cast<T>(1) - c) * axis.z * axis.z;
Result[2][3] = static_cast<T>(0);
Result[3] = tvec4<T, P>(0, 0, 0, 1);
return m * Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> scale(tmat4x4<T, P> const & m, tvec3<T, P> const & v)
{
tmat4x4<T, P> Result(uninitialize);
Result[0] = m[0] * v[0];
Result[1] = m[1] * v[1];
Result[2] = m[2] * v[2];
Result[3] = m[3];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> scale_slow(tmat4x4<T, P> const & m, tvec3<T, P> const & v)
{
tmat4x4<T, P> Result(T(1));
Result[0][0] = v.x;
Result[1][1] = v.y;
Result[2][2] = v.z;
return m * Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
(
T left, T right,
T bottom, T top,
T zNear, T zFar
)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return orthoLH(left, right, bottom, top, zNear, zFar);
# else
return orthoRH(left, right, bottom, top, zNear, zFar);
# endif
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> orthoLH
(
T left, T right,
T bottom, T top,
T zNear, T zFar
)
{
tmat4x4<T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = static_cast<T>(1) / (zFar - zNear);
Result[3][2] = - zNear / (zFar - zNear);
# else
Result[2][2] = static_cast<T>(2) / (zFar - zNear);
Result[3][2] = - (zFar + zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> orthoRH
(
T left, T right,
T bottom, T top,
T zNear, T zFar
)
{
tmat4x4<T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = - static_cast<T>(1) / (zFar - zNear);
Result[3][2] = - zNear / (zFar - zNear);
# else
Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
Result[3][2] = - (zFar + zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
(
T left, T right,
T bottom, T top
)
{
tmat4x4<T, defaultp> Result(static_cast<T>(1));
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = - static_cast<T>(1);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustum
(
T left, T right,
T bottom, T top,
T nearVal, T farVal
)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return frustumLH(left, right, bottom, top, nearVal, farVal);
# else
return frustumRH(left, right, bottom, top, nearVal, farVal);
# endif
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustumLH
(
T left, T right,
T bottom, T top,
T nearVal, T farVal
)
{
tmat4x4<T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][3] = static_cast<T>(1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = farVal / (farVal - nearVal);
Result[3][2] = -(farVal * nearVal) / (farVal - nearVal);
# else
Result[2][2] = (farVal + nearVal) / (farVal - nearVal);
Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustumRH
(
T left, T right,
T bottom, T top,
T nearVal, T farVal
)
{
tmat4x4<T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][3] = static_cast<T>(-1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = farVal / (nearVal - farVal);
Result[3][2] = -(farVal * nearVal) / (farVal - nearVal);
# else
Result[2][2] = - (farVal + nearVal) / (farVal - nearVal);
Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspective(T fovy, T aspect, T zNear, T zFar)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return perspectiveLH(fovy, aspect, zNear, zFar);
# else
return perspectiveRH(fovy, aspect, zNear, zFar);
# endif
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveRH(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][3] = - static_cast<T>(1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = zFar / (zNear - zFar);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
# else
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveLH(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][3] = static_cast<T>(1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = zFar / (zFar - zNear);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
# else
Result[2][2] = (zFar + zNear) / (zFar - zNear);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFov(T fov, T width, T height, T zNear, T zFar)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return perspectiveFovLH(fov, width, height, zNear, zFar);
# else
return perspectiveFovRH(fov, width, height, zNear, zFar);
# endif
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovRH(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][3] = - static_cast<T>(1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = zFar / (zNear - zFar);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
# else
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovLH(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][3] = static_cast<T>(1);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
Result[2][2] = zFar / (zFar - zNear);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
# else
Result[2][2] = (zFar + zNear) / (zFar - zNear);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
# endif
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspective(T fovy, T aspect, T zNear)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return infinitePerspectiveLH(fovy, aspect, zNear);
# else
return infinitePerspectiveRH(fovy, aspect, zNear);
# endif
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspectiveRH(T fovy, T aspect, T zNear)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = - static_cast<T>(1);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = - static_cast<T>(2) * zNear;
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspectiveLH(T fovy, T aspect, T zNear)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
tmat4x4<T, defaultp> Result(T(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = static_cast<T>(1);
Result[2][3] = static_cast<T>(1);
Result[3][2] = - static_cast<T>(2) * zNear;
return Result;
}
// Infinite projection matrix: http://www.terathon.com/gdc07_lengyel.pdf
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear, T ep)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
tmat4x4<T, defaultp> Result(static_cast<T>(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = ep - static_cast<T>(1);
Result[2][3] = static_cast<T>(-1);
Result[3][2] = (ep - static_cast<T>(2)) * zNear;
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear)
{
return tweakedInfinitePerspective(fovy, aspect, zNear, epsilon<T>());
}
template <typename T, typename U, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> project
(
tvec3<T, P> const & obj,
tmat4x4<T, P> const & model,
tmat4x4<T, P> const & proj,
tvec4<U, P> const & viewport
)
{
tvec4<T, P> tmp = tvec4<T, P>(obj, static_cast<T>(1));
tmp = model * tmp;
tmp = proj * tmp;
tmp /= tmp.w;
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
tmp.x = tmp.x * static_cast<T>(0.5) + static_cast<T>(0.5);
tmp.y = tmp.y * static_cast<T>(0.5) + static_cast<T>(0.5);
# else
tmp = tmp * static_cast<T>(0.5) + static_cast<T>(0.5);
# endif
tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]);
tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]);
return tvec3<T, P>(tmp);
}
template <typename T, typename U, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> unProject
(
tvec3<T, P> const & win,
tmat4x4<T, P> const & model,
tmat4x4<T, P> const & proj,
tvec4<U, P> const & viewport
)
{
tmat4x4<T, P> Inverse = inverse(proj * model);
tvec4<T, P> tmp = tvec4<T, P>(win, T(1));
tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]);
tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]);
# if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE
tmp.x = tmp.x * static_cast<T>(2) - static_cast<T>(1);
tmp.y = tmp.y * static_cast<T>(2) - static_cast<T>(1);
# else
tmp = tmp * static_cast<T>(2) - static_cast<T>(1);
# endif
tvec4<T, P> obj = Inverse * tmp;
obj /= obj.w;
return tvec3<T, P>(obj);
}
template <typename T, precision P, typename U>
GLM_FUNC_QUALIFIER tmat4x4<T, P> pickMatrix(tvec2<T, P> const & center, tvec2<T, P> const & delta, tvec4<U, P> const & viewport)
{
assert(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0));
tmat4x4<T, P> Result(static_cast<T>(1));
if(!(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0)))
return Result; // Error
tvec3<T, P> Temp(
(static_cast<T>(viewport[2]) - static_cast<T>(2) * (center.x - static_cast<T>(viewport[0]))) / delta.x,
(static_cast<T>(viewport[3]) - static_cast<T>(2) * (center.y - static_cast<T>(viewport[1]))) / delta.y,
static_cast<T>(0));
// Translate and scale the picked region to the entire window
Result = translate(Result, Temp);
return scale(Result, tvec3<T, P>(static_cast<T>(viewport[2]) / delta.x, static_cast<T>(viewport[3]) / delta.y, static_cast<T>(1)));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAt(tvec3<T, P> const & eye, tvec3<T, P> const & center, tvec3<T, P> const & up)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return lookAtLH(eye, center, up);
# else
return lookAtRH(eye, center, up);
# endif
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtRH
(
tvec3<T, P> const & eye,
tvec3<T, P> const & center,
tvec3<T, P> const & up
)
{
tvec3<T, P> const f(normalize(center - eye));
tvec3<T, P> const s(normalize(cross(f, up)));
tvec3<T, P> const u(cross(s, f));
tmat4x4<T, P> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] =-f.x;
Result[1][2] =-f.y;
Result[2][2] =-f.z;
Result[3][0] =-dot(s, eye);
Result[3][1] =-dot(u, eye);
Result[3][2] = dot(f, eye);
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtLH
(
tvec3<T, P> const & eye,
tvec3<T, P> const & center,
tvec3<T, P> const & up
)
{
tvec3<T, P> const f(normalize(center - eye));
tvec3<T, P> const s(normalize(cross(up, f)));
tvec3<T, P> const u(cross(f, s));
tmat4x4<T, P> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] = f.x;
Result[1][2] = f.y;
Result[2][2] = f.z;
Result[3][0] = -dot(s, eye);
Result[3][1] = -dot(u, eye);
Result[3][2] = -dot(f, eye);
return Result;
}
}//namespace glm
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